Somewhere Stephen Williams once posted a short video clip where the camera was being Dolly-ed in on the subject's face, whilst the zoom was simultaneously widened to precisely cancel the enlargement of the subject's face. That dramatically showed the difference between a subject shot physically close-up, and a similarly dimension-ed shot taken from further away with a telephoto lens.
The shape of the subject's face changes dramatically, and this is one of the several mechanisms your eyes and brain use to build 3-D images.
For example, imagine a scene where an actor walks into a restaurant and spots someone he knows at a table far across the room. The audience aren't going to be able to tell exactly what he is looking at from the initial wide shot, so you would normally cut to a close-up of the table in question. That would normally be done with a long focal length lens from across the room, because that's more or less how the actor would be seeing it (the shape of people's heads, perspective, depth of field etc).
But if the script then calls for the actor to walk over and talk to the people at that table, for that scene you would normally move the camera up to the table and switch to a shorter focal length lens. The change in the way the people's heads are captured then immediately suggests to your brain that the actor is now close to the table.
This is the same reason tracking shots using a dolly are vastly preferable to using a zoom. With the tracking shot, there will be a whole swag of image dimension and perspective changes that suggest to your brain what is actually going on. With a zoomed shot, your brain doesn't really know what it is looking at.
A really dramatic example of this was that in the Iron Man movies, the closeups of Tony Stark's face while he's wearing the Iron Man suit, were done with 65mm format cameras, to give that extreme claustrophobic effect, but without distorting his face too much.